This problem doesn't have anything to do with the vector "u". Why is that given? [itex]D_vf[/itex] is the dot product of the gradient, [itex]\nabla f[/itex], and a unit vector in the same direction as vector v. Since you want that to be 0, you are looking for two unit vectors perpendicular to [itex]\nabla f[/itex].Cpt Qwark said:Homework Statement
For [tex]f(x,y)=x^2-xy+y^2[/tex] and the vector [tex]u=i+j[/tex].
ii)Find two unit vectors such [tex]D_vf=0[/tex]
2. Homework Equations
So "u" was used in previous questions?N/A.
The Attempt at a Solution
Not sure if relevant but the previous questions were asking for the unit vector u - which I got [tex]\hat{u}=\frac{1}{\sqrt{2}}(i+j)[/tex] for the maximum value of [tex]D_uf[/tex] which was [tex]\sqrt{2}[/tex].
Unit vectors are vectors that have a magnitude of 1 and are used to indicate direction in a given space. They are commonly used in mathematics and physics.
To find unit vectors for a function, you need to take the partial derivatives of the function with respect to each variable. Then, you can use those partial derivatives to create a vector and divide it by its magnitude to get a unit vector.
Unit vectors are important in vector calculus because they allow us to represent and manipulate vectors in a more simplified manner. They also help us understand the direction and magnitude of a vector in a given space.
The equation Duf=0 represents the directional derivative of a function in the direction of a given unit vector. By finding unit vectors for a function, we can then use them to calculate the directional derivative and determine the direction in which the function is changing the fastest.
No, unit vectors cannot be negative. As mentioned earlier, they have a magnitude of 1, which means they cannot have a negative value. However, they can indicate a direction that is opposite to the original vector's direction.